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To solve the given problems and find the stationary points, we need to calculate the partial derivatives of the functions with respect to both \(x\) and \(y\). Then, we'll find where both derivatives are equal to zero, and classify the stationary points. ### 1. Function (i): \( f(x, y) = 4xy + x^4 - y^4 \) Step 1: Compute the partial derivatives: \[ \frac{\partial f}{\partial x} = 4y + 4x^3 \] \[ \frac{\partial f}{\partial y} = 4x - 4y^3 \] Step 2: Solve the system of equations: Set both partial _______ __________ ______ _______ _______ ____ _______ _______.
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